performance modelling of fuel cells systems through petri nets

Performance Modelling of

Fuel cells Systems Through Petri Nets

Claudia Fecarotti1, John Andrews1 and Rui Chen2

1 The University of Nottingham , 2 Loughborough University

Hydrogen & Fuel Cell SUPERGEN Researcher Conference University of Birmingham

December 2014

http://www.lboro.ac.uk/

Motivations and Aim of the Research

• FC technology is developed for commercial exploitation in a wide range of applications (automotive, telecommunication, stationary power, etc)

• Reliability and durability are among the main barriers to commercialisation

• The lifetime of a fuel cells stack is difficult to estimate:

• standard engineering measures of lifetime (MTTF) are difficult to specify since fuel cell’s performance degrades gradually and strongly depends on the operating conditions

• Lack of available data on FC behaviour

• Clearly the system performance depends on the reliability of the overall system including both the stack and the balance of plant

This research seeks at introducing a modelling method for the performance analysis of fuel cell systems including the stack and the supporting system, aimed at predicting the system lifetime.


The Fuel Cells System Model

Aim of the model Simulate the operation of the fuel cell stack and its supporting system to predict the system lifetime based on the system structure and the components deterioration processes.

• Malfunctioning and/or failures of components of the BOP affect the operating parameters and in turn the stack performance.

• The model takes into account the causal relationships between the operation of the balance of plant (BOP) and the fuel cell stack performance.

• The stochastic approach accounts for the data uncertainty and variability of voltage

decay rates with operating conditions

Boundaries: Stack + BOP


Modelling Method: Petri Nets

Advantages Models the state of the system

Dynamic system modelling methodology

Models dependencies and concurrencies within the

system

No limit to the level of detail included

Modularization

Any distribution for event times

Operational and purging strategy options can be

switched on and off in the models

Tokens store information and can represent both

continuous and discrete variables

t


The FC System Model-Modular Structure

RR R

RR

P2Actual flow

P1 required flow

P3 incorrect measurement value (lower)

P4 correct measurement value

P5 incorrect measurment value (higher)

P11 valve fails

P12 failure

revealed

P10 valve works

P13inspection

P14No inspection

P9 failure revealed

P8 Sensor failed (high)

P7 Sensor works

P6 Sensor failed

(low)

T4 T3 T2

T5

T6

T7

T13T12

T8 failure

T10repair

T11 repair

T19 inspection starts

T18Inspection

ends

T17 repair

T16

T15failure

T14

T1

T9 failure Control action on the

valve

Sensor measurement

R R R

RR

P16Actual flow

P15 required flow



P19 incorrect measurement value (higher)

P25

P28Failure revealed

P24 Fan works

P23 failure revealed

P22 sensor failed (high)

P21 sensor works

P20sensor failed

(low)

T21 T22 T23

T24

T25

T26

T32T31

T27failure

T28failure

T29repair

T30repair

T40 repair

T38

T35

T33

T20

T37

T34

T39

T36

P26 P27

R

P13inspection

P14No inspection


T18Inspection

ends

Sensor measurement

Control action on the fan

Poss ible failure states of the fan

Poss ib le failures of the fan

R R R

RR

P30Actual

temperature

P29 required temperature




P39


P34 fan works



P36 sensor works

P35 sensor failed (low)

T43 T42 T41

T44

T45

T46

T53T52

T48failure

T49 failure

T50repair

T51repair

T60 repair

T58

T55

T47

T57

T54

T59

T56

P40 P41

R




P13inspection

P14No inspection


T18Inspection

ends

Sensor measurement

R R R

RR

P44Stack relative

humidity

P43 required relative

humidity





P48 humidification system works



P50 Sensor works

P49Sensor

failed (low)

T63 T62 T61

T64

T65

T66

T73T72

T68 T69

T70repair

T71repair

T78 repair

T76

T74 pump failure

T67

T77

T75 valve failure

P53Pump failed

P54 valve failed

R

P16Actual air flow rate

P30 stack

temperatureP70 current drawn

T76

P13inspection

P14No inspection


T18Inspection

ends

Control action on the valve

P2Actual FH2

P16Actual Fai r

P30Actual Tstack

P44Actual RHcell

P56No of s tart-up

cycles

P57Time in OCV

P58Contamination

level (CO)

P70Current drawn

P59Voltage below

threshold

P60Voltage above

threshold

P61Purging

P62

T61

T63T62

T64


The FC System Model – Module example: PN for the Hydrogen Supply System

RR R

RR

P2Actual flow

P1 required flow




P11 valve fails

P12 failure

revealed

P10 valve works

P13inspection

P14No inspection

P9 failure revealed


P7 Sensor works

P6 Sensor failed

(low)

T4 T3 T2

T5

T6

T7

T13T12

T8 failure

T10repair

T11 repair


T18Inspection

ends

T17 repair

T16

T15failure

T14

T1


valve

Sensor measurement

Inspection process

Sensor failure/repair process

Valve failure/repair process

Control action

Flow demand

Flow provided

Sensor measurements


The FC System Model - Modular Structure

RR R

RR

P2Actual flow

P1 required flow




P11 valve fails

P12 failure

revealed

P10 valve works

P13inspection

P14No inspection

P9 failure revealed


P7 Sensor works

P6 Sensor failed

(low)

T4 T3 T2

T5

T6

T7

T13T12

T8 failure

T10repair

T11 repair


T18Inspection

ends

T17 repair

T16

T15failure

T14

T1


valve

Sensor measurement

R R R

RR

P16Actual flow

P15 required flow




P25

P28Failure revealed

P24 Fan works



P21 sensor works

P20sensor failed

(low)

T21 T22 T23

T24

T25

T26

T32T31

T27failure

T28failure

T29repair

T30repair

T40 repair

T38

T35

T33

T20

T37

T34

T39

T36

P26 P27

R

P13inspection

P14No inspection


T18Inspection

ends

Sensor measurement




R R R

RR

P30Actual

temperature

P29 required temperature




P39


P34 fan works



P36 sensor works

P35 sensor failed (low)

T43 T42 T41

T44

T45

T46

T53T52

T48failure

T49 failure

T50repair

T51repair

T60 repair

T58

T55

T47

T57

T54

T59

T56

P40 P41

R




P13inspection

P14No inspection


T18Inspection

ends

Sensor measurement

R R R

RR

P44Stack relative

humidity

P43 required relative

humidity





P48 humidification system works



P50 Sensor works

P49Sensor

failed (low)

T63 T62 T61

T64

T65

T66

T73T72

T68 T69

T70repair

T71repair

T78 repair

T76

T74 pump failure

T67

T77

T75 valve failure

P53Pump failed

P54 valve failed

R

P16Actual air flow rate

P30 stack

temperatureP70 current drawn

T76

P13inspection

P14No inspection


T18Inspection

ends

Control action on the valve

P2Actual FH2

P16Actual Fai r

P30Actual Tstack

P44Actual RHcell

P56No of s tart-up

cycles

P57Time in OCV

P58Contamination

level (CO)

P70Current drawn

P59Voltage below

threshold

P60Voltage above

threshold

P61Purging

P62

T61

T63T62

T64


The FC System Model – The Stack Voltage Module

P2Actual FH2

P16Actual Fai r

P30Actual Tstack

P44Actual RHcell

P56No of s tart-up

cycles

P57Time in OCV

P58Contamination

level (CO)

P70Current drawn

P59Voltage below

threshold

P60Voltage above

threshold

P61Purging

P62

T61

T63T62

T64

Operating parameters

Purging cycle

Stack voltage output gradually decreases as a result of aging and deterioration processes. The voltage decay rate can increase severely as an effect of adverse operating conditions

The voltage is treated as a continuous variable, represented by the value of the token in place P60 (or P59).


Model Analysis

The Petri net is simulated using the Monte Carlo method

• The goal is to estimate the expected system performance (system lifetime) with respect to pre-defined performance criteria (voltage threshold)

• Many simulation are run, each representing one life cycle of the system • Statistics are collected in order to provide an indication of the system

performance • Sampling from a distribution is required for all stochastic transitions in

the Petri net which represent events whose times of occurrence is not deterministic but follows a statistical distribution

• The system lifetime is obtained and recorded in each run, and the

estimate is evaluated as the average over the number of simulations


Model Analysis – System Specification

Input data

• MTTF (and MTTR) of the components of the BOP (to generate times of failures and times for repair)

𝐹 𝑡 = 1 − 𝑒−𝑡

𝑀𝑇𝑇𝐹 = 𝑋 , 𝑋 ∈ 0, 1 , 𝑡 = −𝑀𝑇𝑇𝐹 ∙ ln 𝑋

• Voltage decay rate in the range 1-10 μVh-1 for normal operating

conditions (steady-state operation, Tstack=60-70°C, RH=100%)

• Observed voltage decay rates (data from the literature ranked

according to the operating parameters)

• Inspection frequencies

• Frequencies and duration of purging

voltage decay rate is a random variable


Model Analysis – Simulations and Results

• 5000 simulations have been executed to ensure convergence of results is achieved

• The system operation has been simulated under steady state conditions. Simulations are stopped when the voltage drops below the established threshold and is not recovered to an acceptable value after purging

• At the end of each simulation, the system lifetime is recorded and the expected

value is evaluated providing the system average lifetime

6000

6200

6400

6600

6800

7000

7200

0 1000 2000 3000 4000 5000

Ava

rage

lif

eti

me

(h

)

no of simulations

Plot of average lifetime against the number of simulations (Voltage threshold 3.8V)

6720 h

4 cells stack Threshold is set to 3.8V



Fitting a distribution to the lifetime values generated by the model, it was found that they follow a 3-parameter Weibull distribution

ReliaSoft W eibull++ 7 - www.ReliaSoft.com

F/S Histogram

Period

Va

lue

0-1548 1548-3... 3096-4... 4644-6... 6192-7... 7740-9... 9288-1... 10836-... 12384-... 13932-... 15480-... 17028-... 18576-...0.000

2.000E-4

4.000E-5

8.000E-5

1.200E-4

1.600E-4

FS H istogram

Pdf Line

Failures

John Andrews

University of Nottingham

21/ 10/ 2014

18:59:33

Probability density function (Voltage threshold 3.8V) 𝑓 𝑡 =𝛽 𝑡 − 𝛾 𝛽−1

𝜂𝛽𝑒𝑥𝑝 −

𝑡 − 𝛾

𝜂

𝛽

• η characteristic life, is the life time at which 2/3 of the population will have reached the prescribed threshold.

• β shape parameter gives an

indication of the rate of wear-out of the system.

• γ minimum lifetime, indicates the

minimum lifetime value in the population.

β= 2.7984; η= 5752; γ=1605




Unreliability vs Time Plot

Time, (t)

Un

re

lia

bil

ity

, F

(t)

=1

-R

(t)

0.000 20000.0004000.000 8000.000 12000.000 16000.000

0.000

1.000

0.200

0.400

0.600

0.800

Unreliability

Data 1

W eibull-3P

MLE SRM MED FM

F=5000/ S=0

Data Points

Unreliability Line

John Andrews


21/ 10/ 2014

18:57:38


Failure Rate vs Time Plot

Time, (t)

Fa

ilu

re

Ra

te,

f(t)

/R

(t)

0.000 20000.0004000.000 8000.000 12000.000 16000.000

0.000

0.003

6.000E-4

0.001

0.002

0.002

Failure Rate

Data 1

W eibull-3P

MLE SRM MED FM

F=5000/ S=0

Failure Rate Line

John Andrews


21/ 10/ 2014

18:58:47

Unreliability function System failure rate

𝐹 𝑡 = 1 − 𝑒𝑥𝑝 −𝑡 − 𝛾

𝜂

𝛽

Increasing failure rate due to the wearing-out of the stack as a consequence of ageing and degradation mechanisms

shape parameter β= 2.7984 >1

8000 h

0.76



4.00E+03

6.00E+03

8.00E+03

1.00E+04

1.20E+04

1.40E+04

1.60E+04

1.80E+04

2.5 3 3.5 4

Ava

rage l

ifeti

me (h

)

Voltage threshold (V)

Purging interval 90 mins

Purging interval 60 mins

Voltage threshold Average lifetime Variance Weibull parameters

3.8 6723 2048 β= 2.7984; η= 5752; γ=1605

3.6 9227 2403 β= 2.8846; η= 6998; γ=2986

3.4 11178 2610 β= 3.4574; η= 8781; γ=3281

3.2 12800 2886 β= 2.936; η= 8650; γ=5089

3.0 14246 3012 β= 3.5257; η= 102256; γ=5037

The behaviour of the system for different voltage threshold values and purging frequencies has been also simulated


Conclusions

• The model simulates the operation of the fuel cell stack and its supporting systems taking into account the causal relationships between the operation of the balance of plant and the fuel cell stack performance

• MTTF of BOP components and stack voltage decay rates are input parameters for

the model • Data for voltage decay rates collected from the literature have been used here in

order to demonstrate the capability of the model

• The model is analysed by means of the Monte Carlo method. The stochastic approach allows taking into account data uncertainty and variability

• The modelling process produces distributions of the output parameters (system

lifetime) as an alternative to the point estimates delivered by alternative methods • This enables an appreciation of the best and worst possible output lifetime as well

as the expected system performance


performance modelling of fuel cells systems through petri nets

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